While I agree that trees could cause a problem with the system, I do not think that is worth destroying your landscaping to remove them.
I have 15 each septic systems--been there several years from 20 years on down to ten years--and I have not noticed any problems at all associated with the trees interfering with the septic system--the trees around my septics/laterals are oaks and pecans.
My worse (only) problems have been tenants that use an overabundance of water, and it kills the trees.